Computing the confidence levels for a root‐mean‐square test of goodness‐of‐fit

Computing the confidence levels for a root‐mean‐square test of goodness‐of‐fit

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Article ID: iaor20115674
Volume: 217
Issue: 22
Start Page Number: 9072
End Page Number: 9084
Publication Date: Jul 2011
Journal: Applied Mathematics and Computation
Authors: , ,
Keywords: statistics: distributions
Abstract:

The classic x2 statistic for testing goodness‐of‐fit has long been a cornerstone of modern statistical practice. The statistic consists of a sum in which each summand involves division by the probability associated with the corresponding bin in the distribution being tested for goodness‐of‐fit. Typically this division should precipitate rebinning to uniformize the probabilities associated with the bins, in order to make the test reasonably powerful. With the now widespread availability of computers, there is no longer any need for this. The present paper provides efficient black‐box algorithms for calculating the asymptotic confidence levels of a variant on the classic x 2 test which omits the problematic division. In many circumstances, it is also feasible to compute the exact confidence levels via Monte Carlo simulation.

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